Remote data integrity checking is a crucial technology in cloud computing. Recently, many works focus on providing data dynamics and/or public verifiability to this type of protocols. Existing protocols can support both features with the help of a third-party auditor. In a previous work, Sebé et al. propose a remote data integrity checking protocol that supports data dynamics. In this paper, we adapt Sebé et al.'s protocol to support public verifiability. The proposed protocol supports public verifiability without help of a third-party auditor. In addition, the proposed protocol does not leak any private information to third-party verifiers. Through a formal analysis, we show the correctness and security of the protocol. After that, through theoretical analysis and experimental results, we demonstrate that the proposed protocol has a good performance.